The vector field \(Y\)  is called a distance vector field related to \(p\)  and \( U\) . Let \(x \in \tilde{V}\)  and \(X\in T_{x} N\) . It holds by the similar proof as [1]} that
\(X\Vert Y(x)\Vert _g=\frac{\langle X,Y(x) \rangle _g}{\Vert Y(x)\Vert _g}.\) 
